Problem: What do the following two equations represent? $-3x+3y = 1$ $-15x+15y = -2$
Solution: Putting the first equation in $y = mx + b$ form gives: $-3x+3y = 1$ $3y = 3x+1$ $y = 1x + \dfrac{1}{3}$ Putting the second equation in $y = mx + b$ form gives: $-15x+15y = -2$ $15y = 15x-2$ $y = 1x - \dfrac{2}{15}$ The slopes are equal, and the y-intercepts are different, so the lines are parallel.